The minister for integration, who is a naturalised Italian citizen born in the Democratic Republic of Congo, was giving a speech in the town of Cervia on the Adriatic coast on Friday.

After the bananas narrowly missed the stage, she chided the unknown culprit for "wasting food". On Sunday she said that the unrelenting barrage of hostility since she became minister in April was more vicious than she had anticipated, but would not stop her doing her job.

"I cannot hide that at times I feel tired of the repetition of such serious insults. I did not expect them to be this strong," she told daily newspaper La Repubblica. "But I will not stop or dwell on the attacks themselves. I am trying to look ahead, to reflect on the discomfort that we must understand is behind these incidents and on how politics and society as a whole can best respond."

Since her inclusion in Enrico Letta's grand coalition prompted one MEP in the xenophobic Northern League to brand it a "bongo bongo" government, Kyenge has been the target of repeated racial abuse. Before her arrival in Cervia, police said they had found mannequins daubed with blood-red paint and bearing signs reading: "Immigration kills".

The far-right party Forza Nuova (FN) claimed responsibility for the mannequins but denied having anything to do with the banana throwing. Graffiti daubed on a wall the town of Macerata, near Ancona, in May, however, would appear to show the party is not averse to such actions. It read: "Kyenge, go back to Congo".

Police said on Sunday they were trying to identify who had thrown the bananas.

Asked if the attacks would deter Kyenge from her priorities – which include changing the law to make it easier for children born to immigrants in Italy to gain Italian citizenship – she replied that, on the contrary, they gave her confidence, even if they also made her concerned for the safety and wellbeing of her family. "In a way, the attacks strengthen me and the country," she said. "The reactions to these insults … end up uniting 'good' Italy and will perhaps help to reawaken many consciences which have slightly dozed off in recent years."

The latest incident was roundly condemned by the political mainstream, with expressions of solidarity from her centre-left Democratic Party (PD) and members Silvio Berlusconi's centre-right Freedom People PdL party and the Northern League.

However, in a pointed comment, Kyenge called on her fellow politicians to watch what they say. "Those who take on public roles or political leadership should understand the importance of the words they utter," she said.

Earlier this month, Roberto Calderoli, the League's vice-president in the Senate with a track record of racist and Islamophobic comments, prompted intense controversy when he said the minister reminded him of an orang-utan. Although the remark was condemned furiously by many, including prime minister Letta, who said he should resign, Calderoli remains in his job.

Kyenge, an eye surgeon who was elected as an MP in February, said her experience in recent months showed that there was a need for a nationwide reflection on racism and immigration in Italy. "In other European countries, like Sweden, there are black ministers, but what happens to me in Italy does not happen to them," she said.